Baysian and empirical Bayes (EB) are important statistical methods and havebeen widely applied to many fields of statistics.This report consists of four Chapters.　　In the first part of Chapter one, we construct empirical Bayes (EB) estimatorof parameter β in the general regression model y =Ⅹβ + ε with ε～ N(0, σ2I).　　Based on Pitman closeness (PC) criterion and mean square error matrix (MSEM)criterion, we obtain the superiority of the EB estimator over the ordinary leastsquare estimator (OLSE).　　In the second part of Chapter one, for a system of two seemingly unrelated re-gression equations, using covariance adjusted technique, we propose the parametricBayes and empirical Bayes iteration estimator sequences for regression coefficients.　　We prove that the covariance matrices converge monotonically as well as the con-sistency of the Bayes iteration estimator squence.Based on the Mean Square Error(MSE) criterion, we exhibit the superiority of empirical Bayes iteration estimatorover the Bayes estimator of single equation when the covariance matrix of errors isunknown.The results obtained in this part show further the power of covarianceadjusted approach.　　In the first part of Chapter two, we study the two-action problem in the expo-nential distribution using empirical Bayes (EB) approach.Based on type Ⅱ censoredsamples, we construct an EB test rule and obtain an optimal rate of convergencewhich is better than any other earlier results.　　In the second part of Chapter two, using a linear error loss function, we considerthe one-sided testing problem for one-parameter exponential family via the empiricalBayes (EB) approach.Under the assumption that the historical samples are ran-domly censored from the right, we work out a monotone EB test whose convergencerates can be arbitrarily close to O(n-1) under some suitable conditions.　　Chapter three considers an empirical Bayes prediction problem under randomcensorship.Using censored samples, we construct a prediction interval for a set of in-terest which consists of some unobserved samples.Simulation studies are conductedto exhibit the coverage probabilities of the prediction interval.　　In the part one of Chapter four, we propose a criterion which tells us how tochoose a loss function in Bayesian analysis.　　In the part two of Chapter four, we study the empirical likelihood method for aparametric model which parameterizes the conditional density of a response givencovariate.It is shown the adjusted empirical log-likelihood ratio is asymptoticallystandard X2 when missing responses are imputed using maximum likelihood esti-mate.